Load under sand pile.

I am working on a project where I need to design a tunnel under a large sand pile. Previously I took the area on top of the tunnel and considered the volume directly above the tunnel and calculated the total weight. This may be correct but when considering material in a pile does the force result from a upside down cone shape adding more weight or right side up having the reverse affect where there is less weight than expected?

I would think the force would be perpendicular to the surface. That is, all of the force acts directly towards the center of the pipe. This means, for example, take the "segment" of pipe orientated 30° from the vertical. There will be more sand on top of it, however, only 0.866 (cos30) will be acting towards the center of the pipe. 0.500 (sin30) will act as hoop stress.

I would think one would need to double integrate, once to calculate the total volume on top of the pipe, and then a second time to calculate the other stuff.

Alternately, I would say a reasonable assumption would be to take a differential segment at 45° and find the force at that point. Then average between 0° and 90°. Multiply by two to get the total force on both sides.

......i think.....haha

edit: I should clarify. I think if you just take the volume and find the weight of the sand, that will be your total weight, and total force on the pipe. However, you do not want the total force, you want the force perpendicular to the surface, as that will be your failure point if any.

There was something in Sci. Am., AJP, New Sci., sumpin' probably 15 years ago about this. Number of assumptions: dry sand (aggregate, particles), and a couple others --- bottom line: the forces are transmitted in directions along particle-particle center lines to center and circumference of pile. 'Tain't uniform --- strikes me it's also been used to explain gates at conical bottoms of grain silos getting blown out when designed for hydraulic loads rather than solids.

There was something in Sci. Am., AJP, New Sci., sumpin' probably 15 years ago about this.

Considering that I often have trouble remembering my own name, it surprises me that I seem to recall seeing that (well, I buy it every month, but don't always read all of the articles). Unfortunately, I don't remember what it said and I don't have time to dig through the back issues to try finding it.

Hayne, your link worked for me, but the link that it contained didn't.

As a pool player who relies on physics rather than geometry to calculate shots, this has some relavence to me. The grain-to-grain transfer of force certainly equates to the way the balls on a table move.

I seem to recall from somewhere, though (possibly the aforementioned SA article), that the overall net force is conical due to the fact that all grains are attracted to the centre of the Earth rather than experiencing a truly vertical pull. I don't know how much that would factor in to a small amount of sand, though.

Along the top surface, I would look at the force at any location as equal to the vertical weight of the soil directly above. So at the middle of the top surface, force=density*(h-d). And it is a linear decrease down to force=density*h2 at the left and right side of the top. It is basically just taking vertical equilibrium at every location along the top. It is important to note that there can be a large weight change if the sand becomes saturated with water.

For the horizontal forces, it depends partly on the geotechnical properties of the sand. Normally I would get such information from the geotechnical engineer to derive the horizontal forces. The force at the point is a function of the density, the internal friction properties of the sand, and the amount of sand above that point. You might could make some conservative assumptions about the properties of the sand. Also, if the sand becomes saturated it can have a large effect on the horizontal forces on the walls.

I am working on a project where I need to design a tunnel under a large sand pile. Previously I took the area on top of the tunnel and considered the volume directly above the tunnel and calculated the total weight. This may be correct but when considering material in a pile does the force result from a upside down cone shape adding more weight or right side up having the reverse affect where there is less weight than expected?

I could really overdesign depending on the resluts.

Thanks,
Brian

That seems reasonable to me. In addition to that force directly above the tunnel, you will have compressive forces acting along the sides due to the hydrostatic pressures of the soil.

You need to find information on the angle of repose of sand. It is the angle at which the sand will pile ontop of itself without any barrier. The load would depend on anything past that angle.